Spacetime Existence, Structure, and Expansion Rate from the R12 Rendering Algebra: A Complete Top-Down Derivation with Zero External Physics

Abstract

This paper provides a complete, top-down derivation of the existence, structure, and expansion rate of spacetime entirely from the ℜ₁₂ rendering algebra, using zero external physics.

We answer three fundamental cosmological questions using a single modular Hamiltonian H_mod = 7:

Existence (Q1): Space emerges because the universe's baseline information budget (L = 220) strictly exceeds a single site's processing capacity (N² = 144), mathematically forcing a lattice structure.

Structure (Q2): The algebraic real structure uniquely fixes the KO-dimension, selecting a (3+1) Lorentzian signature.

Expansion (Q3): Cosmic expansion is the irreversible thermodynamic arrow of rendering. We derive the exact Hubble constant (H₀ = 66.18 km s⁻¹ Mpc⁻¹) as an Arrhenius rate of modular vacuum escape, governed by the Landauer information-erasure cost.

No general relativity.
No Friedmann equation.
Zero free parameters.

Everything is derived strictly from the ℜ₁₂ algebra.